John D. Cook • 6/7/2026

Aitken acceleration before Aitken

This article discusses solving Kepler's equation M = E - e sin(E) using fixed-point iteration, comparing Kepler's original method with Peters' 1891 algorithm, which is a special case of Aitken's series acceleration method published in 1926. It demonstrates convergence rates for different eccentricities, showing that Peters' method requires fewer iterations for high accuracy, e.g., for Halley's comet. The content is technical, involving numerical methods, iteration, and convergence analysis relevant to programming and computational mathematics.

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#Numerical Methods #Aitken Acceleration #Fixed Point Iteration